Question

perform the indicated operations & simplify the result. Leave the answer in factored form. ((x/x+4) + 1) / ((12/x^2-16) + 1)

Answer 1

It might be easier to see like this:
\[\frac{\frac{x}{x+4}+1}{\frac{12}{x^{2}-16}+1}\]

Answer 2

yeah, I wasn't sure how to type it in like that :/

Answer 3

No worries.

Answer 4

Actually, I'd probably write it a differnt way initially.

Answer 5

i wouldn't add

Answer 6

\[\left(\frac{x}{x+4}+1\right) \div\ \left(\frac{12}{x^2-16} + 1\right)\]

Answer 7

There. That's much better

Answer 8

Now add, then divide

Answer 9

i would start with
\[\frac{\frac{x}{x+4}+1}{\frac{12}{(x-4)(x+4)}+1}\] and multiply numerator and denominator by \((x+4)(x-4)\) cancelling merrily as i went along

Answer 10

I'm trying to keep it simple @satellite73

Answer 11

\[\frac{\frac{x}{x+4}+1}{\frac{12}{(x-4)(x+4)}+1}\times \frac{(x+4)(x-4)}{(x+4)(x-4)}\]
i think this is simpler, but that is of course a matter of taste

Answer 12

that makes so much sense @satellite73 !!
I didn't even think to factor the other denominator!
been working at this package for far too long

Answer 13

get rid of the compound fraction in one step, then multiply out, combine like terms etc

Answer 14

you get
\[\frac{x(x+4)+(x+4)(x-4)}{12+(x+4)(x-4)}\] and then you can do the algebra top and bottom

Answer 15

\[\left(\frac{x}{x+4}+\frac{x+4}{x+4}\right) \div\ \left(\frac{12}{x^2 - 16} + \frac{x^2 - 16}{x^2 - 16}\right)\]

Answer 16

I was trying to multiply everything by \[x^{2} - 16\] ..silly girl

Answer 17

\[\left(\frac{2x + 4}{x+4}\right) \div\ \left(\frac{x^2 -4}{x^2 - 16} \right)\]

Answer 18

\[\left(\frac{2x + 4}{x+4}\right) \times\ \left(\frac{x^2 -16}{x^2 - 4} \right)\]

Answer 19

And you can still cancel from there

Answer 20

My method isn't too bad either

Answer 21

I wish I could give myself a medal

Answer 22

@refusetofail not silly at all
that is what i did, it is just easier to see if when it is in factored form

Answer 23

so.. wait, I'm kind of confused how to get the actual answer through the simplification..